Frequency generator for radiofrequency equipment and method for generating an output signal

ABSTRACT

A frequency generator generating an output signal having a predetermined output frequency, including: a local oscillator generating a reference signal having a reference frequency, and a phase-locked loop, the phase-locked loop provided with a controlled oscillator generating the output signal having the output frequency as a function of the signal at its input, and a comparator providing a signal to the controlled oscillator as a function of a phase and/or frequency comparison of a first comparison signal based on an input signal applied to a first input of the phase-locked loop with a second comparison signal based on the output signal, the frequency generator further including at least one harmonic generator generating, from the reference signal, a harmonic signal including a predetermined harmonic of the reference signal, the frequency generator applying the harmonic signal of one of the harmonic generators to the first input of the phase-locked loop.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims priority to French Application No. 12 00817,filed Mar. 19, 2012. The French application is incorporated by referencein its entirety.

FIELD OF INVENTION

The invention relates to a frequency generator for radiofrequencyequipment for generating an output signal having a predetermined outputfrequency.

BACKGROUND

In radiofrequency transmission equipment, the output signals generatedby the frequency generator are used to select a channel in the case of atransmission or to assign the equipment to a channel to be used in thecase of reception. For example, an output frequency F_(s) is chosen froma set of predefined discrete frequencies expressed in the formF_(s)=k×ΔF_(s), with kmin≦k≦kmax, k an integer and ΔF_(s) a frequencychosen as a function of the needs of the application.

In a basic architecture, a frequency generator includes a localoscillator for generating a reference signal. This reference signal,which has a reference frequency Fref, is applied to a phase-locked loopin which the reference signal is divided by a first divider. The signalobtained that has a comparison frequency Fcomp is applied to a firstinput of the phase comparator. The output signal from the frequencygenerator is also subject to a frequency division in a second frequencydivider and is then applied to a second input of the phase comparator.The comparator provides the result of the comparison between the firstinput and the second input via a low-pass filter to a voltage-controlledoscillator that generates the output signal with the frequency F_(s) asa function of its input signal. Generally, such frequency generators arecontrolled by a controller that chooses the division ratios of the firstand second divider as a function of the desired output frequency F_(s).

Part of the output signal from the voltage-controlled oscillator isamplified for use by a radiofrequency transmission and/or receptionchain and another part is returned, as previously described, to thecomparator through the second divider.

Such an architecture makes it possible to produce very fine frequencysteps ΔF_(s) relative to the output frequency F_(s). Cases exist inwhich the spectrum delivered by the frequency generator is influenced byparasitic lines, which in particular appear in the case where F_(s) isclose to a harmonic of the reference frequency Fref of the referencesignal directly applied to the phase-locked loop or is close to aharmonic of the comparison frequency Fcomp.

In order to offset this drawback, the architecture previously describedis often modified by adding an additional circuit between the localoscillator and the phase-locked loop, for example a basic circuit of adirect digital synthesizer (DDS) or a second phase-locked loop. Thisadditional circuit is also controlled by the controller so as toeliminate cases of unfavorable relationships between the referencefrequency Fref applied to the phase-locked loop, the comparisonfrequency Fcomp and the output frequency F_(s).

Nevertheless, such a solution requires a complex additional circuit thatcauses significant additional consumption and an unacceptable spacerequirement for the use of such a frequency generator in portableequipment. Furthermore, the additional circuit for generating a variablereference frequency causes a deterioration of the quality of the signalgenerated by the additional circuit compared to that of the originalreference signal.

SUMMARY

The object of the application is to propose a frequency generator and amethod that produce an output signal that is very little disturbedhaving a low-consumption and compact circuit.

This object is achieved, according to the invention, by a frequencygenerator for radiofrequency equipment for generating an output signalhaving a predetermined output frequency, the frequency generatorincluding: a local oscillator to generate a reference signal having areference frequency, a phase-locked loop, the phase-locked loop beingprovided with a controlled oscillator generating the output signalhaving the output frequency as a function of the signal at its input,and a comparator providing a signal to the controlled oscillator as afunction of a phase and/or frequency comparison of a first comparisonsignal based on an input signal applied to a first input of thephase-locked loop with a second comparison signal based on the outputsignal, the frequency generator also including at least one harmonicgenerator adapted to generate, from the reference signal, a harmonicsignal including a predetermined harmonic of the reference signal, thefrequency generator being adapted to apply the harmonic signal of one ofthe harmonic generators to the first input of the phase-locked loop.

According to advantageous features:

-   -   the phase-locked loop is also provided with a first frequency        divider, the first frequency divider being adapted to divide the        frequency of the input signal to generate the first comparison        signal, and/or a second frequency divider, the second frequency        divider being adapted to divide the output frequency of the        output signal to generate the second comparison signal;    -   the harmonic generator is adapted to generate an odd harmonic of        the reference signal;    -   the harmonic generator includes a device adapted to generate a        plurality of harmonics of the reference signal, in particular a        plurality of odd harmonics, for example a generator of a square        signal having the reference frequency of the reference signal,        and a device for extracting a harmonic adapted to select the        predetermined harmonic to be generated by the harmonic        generator;    -   the local oscillator is connected by at least two parallel paths        and at least one switch to the first input of the phase-locked        loop, the switch(es) being adapted to select one of the paths;    -   a first switch is connected between the local oscillator and the        at least two paths, and a second switch is connected between the        at least two paths and the first input of the phase-locked loop;    -   it is adapted to apply the reference signal having the reference        frequency to the first input upon selection of a first path;    -   at least one second path provided with one of the harmonic        generators is such that, when a second path is selected, the        harmonic signal is applied to the first input; and/or    -   the frequency generator also includes a selector adapted to        choose one of the paths as a function of the output frequency of        the output signal to be generated.

Furthermore, this aim is achieved, according to the invention, using amethod for generating an output signal having a predetermined outputfrequency by using a local oscillator to generate a reference signalhaving a reference frequency and a phase-locked loop, the phase-lockedloop being provided with a controlled oscillator generating the outputsignal having the output frequency as a function of a signal at itsinput, and a comparator providing a signal to the controlled oscillatoras a function of a phase and/or frequency comparison of a firstcomparison signal based on an input signal applied to a first input ofthe phase-locked loop with a second comparison signal based on theoutput signal, the method including: selecting a frequency to be appliedto the first input among the reference frequency of the local oscillatorand a predetermined harmonic frequency of the reference signal; thegeneration, from the reference signal, of a harmonic signal having thepredetermined harmonic frequency of the reference signal; and theapplication of the harmonic signal to the first input of thephase-locked loop.

According to advantageous features:

-   -   the selection of the frequency to be applied to the first input        is done as a function of the output frequency of the output        signal.

BRIEF DESCRIPTION OF THE DRAWINGS

Other advantageous features of the present invention will emerge fromthe description thereof provided below, with reference to the drawings,which illustrates one non-limiting example embodiment in which:

FIG. 1 is a schematic circuit of a frequency generator for aradiofrequency transmission or reception equipment,

FIG. 2 is a circuit for generating a harmonic of the frequency generatorof FIG. 1, and

FIG. 3 shows a flowchart of a method according to an example of theinvention.

DETAILED DESCRIPTION

The frequency generator 1 of FIG. 1 is used in radiofrequency equipmentfor a transmission or reception from a radiofrequency channel. Thefrequency generator 1 generates an output signal having an outputfrequency F_(s). The output signal is used, in case of transmission, toselect a predetermined channel, or, in case of reception, to assign theequipment to a predetermined channel. The output frequency F_(s) ischosen from a set of predefined discrete frequencies having a gap ΔF_(s)between them expressed in the form of F_(s)=k×ΔF_(s), with kmin≦k≦kmax,k an integer, and ΔF_(s) a frequency chosen as a function of the needsof the application.

The frequency generator 1 includes a local oscillator 3 that generates areference signal having a reference frequency Fref, a phase-locked loop5, a harmonic generator 7 adapted to generate a predetermined harmonicof a signal provided to the harmonic generator, an amplifier 9 toamplify the output signal, and a controller 11.

First, the phase-locked loop 5 is outlined, then the circuit includingthe harmonic generator 7 arranged between the local oscillator 3 and thephase-locked loop 5.

The phase-locked loop 5 including an electronic component 15, forexample a chip, provided with a first input 16 connected to a firstdivider 17, a second input 18 connected to a second divider 19, and aphase or frequency comparator 21.

The first input 16 of the phase-locked loop is connected to the firstdivider 17 to provide it with an input signal having the input frequencyFe. The first divider 17 is adapted to divide the input frequency Fe togenerate, at its output, a first comparison signal having the comparisonfrequency Fcomp1. The output of the first divider 17 is connected to afirst input 22 a of the phase comparator 21. The division ratio of thefirst divider 17 is R. Therefore, Fcomp1=Fe/R.

The second divider 19 is adapted to divide a frequency of a loop signalFb that is applied to the second input 18 of the phase-locked loop togenerate, at its output, a second comparison signal having thecomparison frequency Fcomp2. The output of the second divider 19 isconnected to a second input 22 b of the phase comparator 21. Thedivision ratio D of the second divider 19 is variable. For example, thesecond divider 19 is a fractional divider. Therefore, Fcomp2=Fb/D.

The phase comparator 21 is adapted to compare the phases and/orfrequencies of the signal supplied to its first input 22 a and itssecond input 22 b, in particular Fcomp1 and Fcomp2. As a function of thecomparison C between Fcomp1 and Fcomp2, the phase comparator 21 isadapted to generate a control voltage signal at its output. The outputof the phase comparator 21 is connected to a low-pass filter 23 of thephase-locked loop 5.

The phase-locked loop 5 also includes a voltage-controlled oscillator 25(VCO). The low-pass filter 23 is connected to the voltage-controlledoscillator 25 to provide the latter with the filtered control signal.The voltage-controlled oscillator 25 is an oscillator wherein the outputfrequency varies as a function of the voltage of the filtered controlsignal. The voltage-controlled oscillator 25 is adapted to generate theoutput signal having the output frequency F_(s).

The output of the voltage-controlled oscillator 25 is connected on theone hand to the amplifier 9 and on the other hand to the second input 18of the phase-locked loop 5. The loop signal then corresponds to theoutput signal, therefore Fb=F_(s). The output frequency F_(s) is thendivided by the second divider 19 to be applied to the second input 22 bof the phase or frequency comparator 21. Then, Fcomp2=F_(s)/D.

The amplifier 9 is adapted to amplify the output signal to provide it toa reception and/or transmission channel of the equipment.

The controller 11 controls the phase-locked loop 5, in particular to setthe division ratios R, D of the first divider 17 and the second divider19 as a function of the desired output frequency F_(s). The controller11 is, in another embodiment, a field programmable gate array (FPGA).For example, the controller 11 has stored a table in its memory inwhich, for each output frequency F_(s), the input signal to be applied,the division ratio R of the first divider 17 and/or the division ratio Dof the second divider 19 are stored. For example, the table is generatedupon design of the frequency generator 1.

During the operation of the phase-locked loop, the second comparisonsignal is locked in on the frequency and phase of the first comparisonsignal due to the effects of the self-regulation of the phase-lockedloop. Therefore, Fcomp1=Fcomp2.

The circuit including the harmonic generator 7 arranged between thelocal oscillator 3 and the phase-locked loop 5 is explained below.

The frequency generator 1 includes two switches 27, 29 adapted to switchon command from the controller between a first path 31 and a second path33 that selectively connect the first switch 27 to the second switch 29.The first switch 27 is connected at the output of the local oscillator3, and the second switch 29 is connected to the first input 16 of thephase-locked loop 5. Therefore, the local oscillator 3 is adapted toprovide the reference signal to the first switch 27, which guides itthrough one of its channels 31, 33 to the second switch 29, then to thefirst input 16.

The harmonic generator 7 is arranged in a first path 33. The harmonicgenerator is then adapted of generating a harmonic signal having asingle harmonic frequency F_(H) of the reference signal. The switches27, 29 are arranged upstream and downstream from the harmonic generator7 in the direction of the reference signal. The second switch 29 thenconnects the harmonic generator 7 to the phase-locked loop 5, inparticular to its first input 16.

The first path 31 is a direct connection, without processing the signalpassing through that path, between the first switch 27 and the secondswitch 29.

In this way, either the reference signal is provided by the second path33 to the harmonic generator 7 and the harmonic signal is applied to thefirst input 16 of the phase-locked loop 5, or the reference signal isdirectly applied to the first input 16 of the phase-locked loop 5 by thefirst path 31.

The two switches 27, 29 and the harmonic generator 7 are controlled bythe controller 11. Therefore, the controller 11 is adapted to select oneof the paths 31, 33. Furthermore, the controller 11 is adapted to startand stop at least a portion of the harmonic generator 7.

The local oscillator 3 is connected to the controller 11 to provide itwith the reference signal.

When the frequency generator is designed, the first path 31 and thesecond path 33 are physically separated to avoid parasitic couplingsbetween them. Furthermore, the local oscillator 3 is well separated fromthe component 15 of the phase-locked loop 5 to prevent disruptions ofthe output signal, in particular when a harmonic of the reference signalis used as input signal.

For example, to that end, an isolating wall for the electromagneticwaves is installed between the first path and the second path, as wellas between the local oscillator 3 and the component 15.

In one embodiment, a plurality of harmonic generators 7 is arranged inparallel, each in a path. Each harmonic generator generates a particularharmonic. In this embodiment, the switches are adapted to choose one ofthe paths to apply one of the harmonics or the reference signal to thefirst input 16 of the phase-locked loop 5. This embodiment allows alarger number of configurations.

The harmonic generator 7 is adapted to be started quickly and stoppedwhen the second path 33 is not used, so as to decrease consumption andthe crosstalk problems that could reduce the performance of thefrequency generator according to the invention. For example, thecontroller 11 is adapted to completely or partially stop the harmonicgenerator 7. The switches 27, 29 do not consume anything when idle. Thecomponents to produce the first path 31 and the second path 32 cause anegligible overall cost increase for a radiofrequency equipment.

FIG. 2 shows an example of a harmonic generator 7. The harmonicgenerator 7 generating a single harmonic includes a device forgenerating a plurality of harmonics 35, 37 and an extraction device 39for selecting one of the harmonics.

For example, the device for generating a plurality of harmonics is asquare signal generator 35 including a logic gate 37, for example alogic inverter 37. The harmonic generator 7 includes a capacitor C1 atits input and is connected to the input of the logic inverter 37. Thereference signal is injected at the capacitor C1. A first resistance R1is connected in parallel with the logic inverter 37. The square signalgenerator 35 is adapted to create a square signal. The spectrum of anideal square signal includes only odd harmonics. However, the realspectrum also includes even harmonics. An optional resistance R2 isadapted to perfect the cyclic ratio of the square signal while erasingor minimizing, as much as possible, the power of the even harmonics toobtain as pure a spectrum as possible. When the harmonic generator isstopped or turned off, its active components, here the logic gate 37,are turned off.

The output of the generator of the square signal 35 is connected to theextraction device 39, here a low-pass filter 39 adapted to select one ofthe generated harmonics. For example, the low-pass filter is centered onthe frequency of the harmonic to be selected.

In one embodiment, instead of a fixed low-pass filter 39, a variablelow-pass filter 39 is used that is locked in by the controller 11. Inthis way, the frequency generator has a larger number of frequencychoices to be applied to the first input 16 of the phase-locked loop 5.

The operation of the frequency generator 1 is explained below.

The frequency generator 1 is adapted to choose a value of Fcomp1 and Fesuch that F_(s) is not close to a multiple of those frequencies.Therefore, the case where F_(s) is approximately equal to k×Fe or F_(s)is approximately equal to 1×Fcomp1, with k,l, integers must be avoided.

Generally, the output frequency F_(s) of the output signal of thefrequency generator 1 is:

F_(s)=Fcomp1×D, with Fcomp1=Fe/R and D=N+Frac/Mod, with Fe being theinput frequency of the input signal of the phase-locked loop, R beingthe division ratio applied to the input frequency Fe by the firstdivider 17, and N and Frac/Mod respectively being the whole portion andthe fractional portion of the division ratio of the second divider 19applied to the output signal having the frequency F_(s). Fcomp1 is thefrequency at which the comparison is done, i.e., the frequency of thefirst comparison signal.

For example, to change the output frequency, the division ratio D of thesecond divider 19 is modified. The distance between two adjacentdiscrete frequencies to be generated then depends on the frequencyFcomp1 of the first comparison signal of the reference frequency and, inthe case of a fractional division, the denominator Mod of the fractionalportion of the division ratio D of the second divider 19. For example,in the case of a whole division ratio D, the distance between twoadjacent discrete frequencies is ΔF_(s)=Fcomp1. In the case of afractional division ratio D (D=N+Frac/Mod), the distance between twoadjacent discrete frequencies to be generated is ΔF_(s)=Fcomp1/Mod.

The distance ΔF_(s) is, in the described embodiment, very fine withrespect to the output frequency F_(s). For example, ΔF_(s) isapproximately 25 kHz for an output frequency F_(s) of several hundredMHz.

Below, one example is provided using the flowchart of FIG. 3 for thecase where the frequency generator 1 must synthesize a frequency F_(s)approximately equal to 10·Fref. The frequency to be synthesized F_(s) isdetermined in step 100.

The exact frequency F_(s) will be F_(s)=10·Fref+Δf, with Δf=n×ΔF_(s)close to 0 relative to F_(s) (n being an integer), as F_(s) is muchgreater than ΔF_(s). When the output frequency is close to a multiple ofFref, the spectrum will be polluted by lines at F_(s)±Δf.

The controller decides in step 102 whether the reference signal havingthe reference frequency Fref is directly applied to the first input 16of the phase-locked loop 5 or if a harmonic of the reference signalgenerated by the harmonic generator 7 is applied to the first input 16of the phase-locked loop 5.

In the case of the example, the controller 11 decides to apply an oddharmonic to the reference frequency Fref of the local oscillator 3, forexample the third harmonic. Then, F_(H)=3·Fref.

Subsequently, in step 104, the controller 11 commands the switches 27,29 such that the reference signal of the local oscillator 3 is appliedto the harmonic generator 7. Furthermore, the controller starts theharmonic generator 7. During the operation of the harmonic generator 7,the logic inverter 37 creates a square signal including the oddharmonics of the reference signal. Therefore, the signal at the outputof the inverter 37 includes harmonic lines at frequenciesF_(c)=(m+1)·Fref, with m an integer. Then, the square signal is filteredby the low-pass filter 39, which is, for example, centered on the thirdharmonic. The harmonic signal at the output of the harmonic generator 7then has a frequency F_(H)=3·Fref. The input signal at the phase-lockedloop 5 therefore has a frequency Fe=3·Fref.

In step 106, the division ratios R, D for the first divider 17 and forthe second divider 19 are applied in a phase-locked loop 5. In oneembodiment, the division ratio of the first divider 17 is an integer,for example 2. Therefore, the controller 11 chooses the division ratiosR, D of the first and second divider as a function of the desired outputfrequency F_(s), for example from values stored in the table in thememory of the controller 11.

The frequency of the first comparison signal at the first input 22 a ofthe first comparator 21 is Fcomp1=Fe/2=3·Fref/2, using R=2.

In that case, it is possible to calculate the deviation between theoutput frequency F_(s) and the closest harmonic of Fe:F _(s)=10·Fref+Δf=10·Fe/3+Δf=3·Fe+⅓·Fe+Δf.

The deviation between the output frequency F_(s) and the closestharmonic of the input frequency Fe used is then ⅓Fe+Δf.

Without applying the harmonic generator, the deviation between theclosest harmonic of the input frequency Fe=Fref could be Δf, asFs=10ΔFref+Δf=10·Fe+Δf.

Therefore, the deviation between the closest harmonic of the inputsignal used and the frequency of the output signal is increasedconsiderably.

The frequency response of the phase-locked loop (PLL) behaves like alow-pass, the cutoff frequency being much lower than Fe, for exampleless than Fe/3. This effect naturally attenuates the lines having adistance greater than ⅓Fe+Δf from F_(s).

Likewise, it is possible to calculate the deviation between the outputfrequency F_(s) and the closest harmonic of Fcomp1:F _(s)=10·Fref+Δf=10.2·Fcomp1/3+Δf=7·Fcomp1+(−⅓·Fcomp1+Δf), withFref=2·Fcomp⅓

Therefore, the deviation between F_(s) and the closest harmonic of thecomparison frequency Fcomp1 used is ⅓·Fcomp1−Δf. Without using theharmonic generator, the deviation between the closest harmonic of thecomparison frequency Fcomp1 and the output frequency F_(s) would only beΔf, as F_(s)=10·Fref+Δf=20·Fcomp1+Δf.

This example demonstrates that the direct application of the frequencyof the reference oscillator leads to an unfavorable case. The use of anodd harmonic of that same frequency resolves the problem.

If the controller decides in step 102, as a function of the desiredoutput frequency F_(s), that the reference signal having a referencefrequency Fref is directly applied to the first input 16 of thephase-locked loop 5, in step 104 the controller 11 commands the switches27, 29 to select the first path 31. Furthermore, the controller turnsoff the harmonic generator 7.

Then, in step 106, the division ratios R, D for the first divider 17 andthe second divider 19 are applied.

According to the invention, the selection of the path 31, 33 is done bythe controller 11, which switches the correct path 31, 33 as a functionof the desired output frequency F_(s).

One advantage of this approach lies in the fact that no significantdeterioration of the noise on the reference frequency of the localoscillator 3 is introduced. The frequency generator and the methodaccording to the invention therefore make it possible to resolve theproblems of lines on the synthesized frequency without deteriorating theoverall performance of the noise of the frequency generator.

The invention claimed is:
 1. A frequency generator for radiofrequencyequipment for generating an output signal having a predetermined outputfrequency, the frequency generator comprising: a local oscillator togenerate a reference signal having a reference frequency, a phase-lockedloop, the phase-locked loop provided with a controlled oscillatorgenerating the output signal having the output frequency as a functionof the signal at its input, and a comparator providing a signal to thecontrolled oscillator as a function of at least one of a phase orfrequency comparison of a first comparison signal based on an inputsignal applied to a first input of the phase-locked loop with a secondcomparison signal based on the output signal, wherein the frequencygenerator also includes at least one harmonic generator adapted togenerate, from the reference signal, a harmonic signal including apredetermined harmonic of the reference signal, the frequency generatorbeing adapted to apply the harmonic signal of one of the harmonicgenerators to the first input of the phase-locked loop.
 2. The frequencygenerator according to claim 1, wherein the phase-locked loop is alsoprovided with a first frequency divider, the first frequency dividerbeing adapted to divide the frequency of the input signal to generate atleast one of the first comparison signal, or a second frequency divider,the second frequency divider being adapted to divide the outputfrequency of the output signal to generate the second comparison signal.3. The frequency generator according to claim 1, wherein the harmonicgenerator is adapted to generate an odd harmonic of the referencesignal.
 4. The frequency generator according to claim 1, wherein theharmonic generator comprises an harmonic device adapted to generate aplurality of harmonics of the reference signal, in particular aplurality of odd harmonics, for example a generator of a square signalhaving the reference frequency of the reference signal, and anextraction device extracting a harmonic adapted to select thepredetermined harmonic to be generated by the harmonic generator.
 5. Thefrequency generator according to claim 1, wherein the local oscillatoris connected by at least two parallel paths and at least one switch tothe first input of the phase-locked loop, the switch being adapted toselect one of the paths.
 6. The frequency generator according to claim5, wherein a first switch is connected between the local oscillator andthe at least two paths, and a second switch is connected between the atleast two paths and the first input of the phase-locked loop.
 7. Thefrequency generator according to claim 5, wherein it is adapted to applythe reference signal having the reference frequency to the first inputupon selection of a first path.
 8. The frequency generator according toclaim 5, wherein at least one second path provided with one of theharmonic generators is such that, when a second path is selected, theharmonic signal is applied to the first input.
 9. The frequencygenerator according to claim 5, further comprising a selector adapted tochoosing one of the paths as a function of the output frequency of theoutput signal to be generated.
 10. A method for generating an outputsignal having a predetermined output frequency by using a localoscillator to generate a reference signal having a reference frequencyand a phase-locked loop, the phase-locked loop being provided with acontrolled oscillator generating the output signal having the outputfrequency as a function of a signal at its input, and a comparatorproviding a signal to the controlled oscillator as a function of a phaseand/or frequency comparison of a first comparison signal based on aninput signal applied to a first input of the phase-locked loop with asecond comparison signal based on the output signal, the methodcomprising the steps of: selecting a frequency to be applied to thefirst input among the reference frequency of the local oscillator and apredetermined harmonic frequency of the reference signal; generating,from the reference signal, a harmonic signal having the predeterminedharmonic frequency of the reference signal; and applying the harmonicsignal to the first input of the phase-locked loop.
 11. The methodaccording to claim 10, wherein the selecting of the frequency to beapplied to the first input is done as a function of the output frequencyof the output signal.